ABSTRACT

It is then relevant to look at the irreducible unitarizable highest weight Vir-modules, i.e., modules 'V on which the action of L0 can be diagonalized:

such that:

As in the Kac-Moody case, let us build the Verma module, M(E, z), for given values of E and z. With respect to the action of L0 , M(E, z) splits as

and

(ii) For z > 1, the Verma module is unitarizable for any E ~ 0, and irreducible.